\section{Insurer Operating Results By Population Loss Ratio Estimate}
\label{sec:InsurerOperatingResultsByPopulationLossRatioEstimate}

Insurers' variable Claims Costs determine whether they succeed or fail: Are they profitable? Are they incurring operating losses? Are they solvent? What level of benefits can they provide? What are the highest level of Claims Costs they can pay and survive? Insurers earn profits if their PLREs and Operating Expense ratios sum to less than 100\% (i.e. Claims Costs + Operating Expenses $<$ Earned Premiums) or they incur Operating Losses. If Claims Costs and Operating Expenses greatly exceed Earned Premiums insurers may be insolvent, unable to pay their obligations. 

\subsection{Insurer Operating Results By Population Loss Ratio Estimate - Profits}
\label{sec:InsurerOperatingResultsByPopulationLossRatioEstimate-Profits}

All insurers earn profits according to these relationships:
\begin{center}
\noindent Profit $\geq$ (Profit Margin + Risk Premium) IF Claims Costs $\leq$ Expected Claims Costs \newline

\noindent Profit $\geq$ Profit Margin IF Claims Costs $\leq$ (Expected Claims Costs + Risk Premium) \newline

\noindent Profit $\geq$ 0 IF Claims Costs $\leq$ (Expected Claims Costs + Profit Margin + Risk Premium) 
\end{center}

\subsection{Insurer Operating Results By Population Loss Ratio Estimate - Losses}
\label{sec:InsurerOperatingResultsByPopulationLossRatioEstimate-Losses}

Insurers incur Operating Losses (Claims Costs $>$ Expected Claims Costs + Profit Margins + Risk Premiums) and become insolvent when they have insufficient resources to pay all their obligations. Insolvent insurers should close their doors, but may continue for many years, as may insolvent health care providers. Insolvent insurers (health care providers) put policyholders (patients) at great risk for denied or delayed care due to insurer (provider) malfeasance or negligence.

Insurers can prevent some insolvencies by maintaining highly liquid assets (``Surplus'') to cover excessive Claims Costs, but no insurer can prevent all risk of insolvency because the highly liquid assets devoted to Surplus are not available to produce goods or services. More Surplus decreases insurers' insolvency risks and profits. Most States have minimal statutory Surplus requirements, but this offers different levels of insolvency risk. I require all insurers to protect against insolvency with probability 0.9987, by maintaining Surplus assets sufficient to cover all Claims Cost from PLREs at, or below three standard errors above the Population Loss Ratio. 

